Unmixing Mineral Abundance and Mg# With Radiative Transfer Theory: Modeling and Applications

Abstract

AbstractMineral abundance and Mg# (100× molar Mg/(Mg + Fe)) are significant in understanding the crustal composition and thermal history of the Moon. In this study, we derive a new set of optical constants for olivine, orthopyroxene, and clinopyroxene using radiative transfer equations that include soil porosity and the opposition effect. Based on the new optical constants, we develop a mineral abundance and Mg# unmixing model, and build a spectral library composed of mineral mixtures of plagioclase, olivine, low‐Ca pyroxene (LCP) and high‐Ca pyroxene (HCP), and Mg# ranging within 40–90. The accuracy of this model in estimating mineral abundance and chemistry is better than 3 vol% for olivine, LCP and HCP, better than 6 vol% for plagioclase, and better than 10 for Mg#. This model is validated using forward and inverse modeling. For the forward modeling, we reproduce the spectra of powdered pure minerals and Lunar Sample Characterization Consortium (LSCC) lunar soils, and the modeled spectra are consistent with those measured in the laboratory. For the inverse modeling, we determined mineral abundances and Mg# of 19 LSCC soil spectra by searching the best match to the spectral library. The modeled mineral abundances of LSCC soils are consistent with those measured by X‐ray digital imaging. We derived a global Mg# map using our model and Moon Mineralogy Mapper images, and our Mg# map shows a peak concentration at 70, consistent with that measured by the Lunar Prospector gamma‐ray spectrometer.